Browse > Article

Modeling on asymmetric circular data using wrapped skew-normal mixture  

Na, Jong-Hwa (Department of Information and Statistics, Chungbuk National University)
Jang, Young-Mi (Korea Health and Welfare Information Service)
Publication Information
Journal of the Korean Data and Information Science Society / v.21, no.2, 2010 , pp. 241-250 More about this Journal
Abstract
Over the past few decades, several studies have been made on the modeling of circular data. But these studies focused mainly on the symmetrical cases including von Mises distribution. Recently, many studies with skew-normal distribution have been conducted in the linear case. In this paper, we dealt the problem of fitting of non-symmetrical circular data with wrapped skew-normal distribution which can be derived by using the principle of wrapping. Wrapped skew-normal distribution is very flexible to asymmetical data as well as to symmetrical data. Multi-modal data are also fitted by using the mixture of wrapped skew-normal distributions. To estimate the parameters of mixture, we suggested the EM algorithm. Finally we verified the accuracy of the suggested algorithm through simulation studies. Application with real data is also considered.
Keywords
Circular data; mixture distribution; wrapped skew-normal;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Pewsey, A. (2000a). The wrapped skew-normal distribution on the circle. Communications in Statistics: Theory and Methods, 29, 2459-2472.   DOI   ScienceOn
2 Pewsey, A. (2000b). Problems of inference for Azzalini's skew-normal distribution. Journal of Applied Statistics, 27, 859-870.   DOI   ScienceOn
3 Azzalini, A. (1985). A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12, 171-178.
4 Fisher, N. I. (1993). Statistical analysis of circular data, Cambridge University Press.
5 Azzalini, A. and Capitanio, A. (1999). Statistical applications of the multivariate skew-normal distribution. Journal of the Royal Statistical Society, Series B, 91, 579-602.
6 Batschelet, E. (1981). Circular statistics in biology, Academic Press, London.
7 Catchpole, E. A. and Morgan, B. J. T. (1997). Detecting parameter redundancy. Biometrika, 84, 187-196.   DOI   ScienceOn
8 Jammalamadaka, S. R. and SenGupta, A. (2001). Topics in circular statistics, World Scientific.
9 Jang, Y. M., Yang, D. Y., Lee, J. Y. and Na, J. H. (2007). Modelling on multi-modal circular data using von mises mixture distribution. The Korean Communications in Statistics, 14, 517-530.   과학기술학회마을   DOI   ScienceOn
10 Mardia, K. V. (1972). Statistics of directional data, Academic Press, New York.
11 Mardia, K. V. and Jupp, P. E. (1999). Directional statistics, Wiley.
12 Nelder, J. A. and Mead, R. (1965). A simplex method for function minimization. Computer Journal, 7, 308-313.   DOI
13 Papakonstantinou, V. (1979). Bietrage zur zirkularen statistik , Ph. D. Dissertation, University of Zurich, Switzerland.